International Relative Price Levels: A Look Under the
Hood

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Abstract:

This paper examines the structure of international relative
price levels using purchasing power parities (PPP) at the
product-level from the 2005 World Bank's International Comparison
Program (ICP). Our examination is motivated by questions arising
from two applications using economy-wide PPPs: the measurement of
real effective exchange rates (REERs) and the correlation between
prices and development. Specifically, how would our view on
competitiveness be affected if one were to use PPP measures that
exclude non-tradable categories? Is it the case that an increase in
per-capita income raises the prices of non-tradable categories?
These questions are not new. What is new here is the use of
relative price levels (as opposed to indexes) at the product
level for 144 countries that differ greatly in their level of
development.

1 Introduction

This paper examines the structure of international relative
price levels using purchasing power parities (PPP) at the
product-level from the 2005 World Bank's International Comparison
Program (ICP). Our examination is motivated by questions arising
from two applications using the familiar economy-wide PPPs: the
measurement of real effective exchange rates (REERs) and the
correlation between prices and development.2

Economy-wide PPPs provide information on international relative
price levels and hence capture a dimension of competitiveness not
incorporated in indexes that measure price changes alone.3 But a
relevant question, so far neglected, is how would our view on
competitiveness be affected if one were to use PPP measures that
exclude non-tradable categories? In addition, since it is
acknowledged that prices for some categories are particularly
difficult to compare across countries, to what extent are PPP-based
GDP price comparisons being influenced by the readings on these "comparison-resistant" categories? Our calculations indicate that
excluding comparsion-resistant categories halves the measured
difference between U.S. prices and the prices of its major trading
partners; excluding non-tradable categories eliminates the
difference entirely. The obvious question raised by this finding is
which measure is better for making inferences about international
competitiveness: the measure including all the expenditure
categories or the narrower measures including only tradable or
comparable products? Though we do not have a definitive answer to
this question, we follow Keynes (1925) and Corden (1994) and show
that prices for non-tradable and comparison-resistant categories
play an integral role in measuring international
competitiveness.

The correlation between aggregate prices and development, known
as the Penn Effect, has been examined extensively. The conventional
explanation for this correlation is that as development expands,
demand across all expenditure categories increases, which raises
the prices of non-tradables but not the prices of tradables because
these are determined in world markets. This explanation raises an
interesting question: is it the case that an increase in per-capita
income raises the relative prices of non-tradable categories? This
question has not been addressed before and an answer to it is of
interest because finding that these correlations are absent would
undermine the conventional explanation for the Penn Effect. To be
sure, interest in disaggregation is not new.4 What is new here is
the use the relative price levels (as opposed to indexes) at
the product level for 144 countries that differ greatly in their
level of development.

The next section describes the data; section 3 lays out the
basic constructs of our PPP-based REER and demonstrates its
sensitivity to the exclusion of non-tradable and non-comparable
categories. Section 4 reports the results from regressions relating
the within-product relative prices to relative incomes. Section 5
offers a few concluding thoughts.

2 Data Description

2.1 ICP Data

The ICP provided the 2005 benchmark purchasing power parities
for 146 countries and 126 basic headings;5 a " basic heading" is
the lowest level of disaggregation for which PPPs are
computed.6 The ICP also provided country data on
population, market exchange rates, the 2005 values for GDP, PPPs
for GDP, and expenditures on each basic headings; these
expenditures add up to GDP.

Reliance on the 2005 ICP benchmarks has several advantages.
First, they are the first to include actual price observations for
China, and the first since 1985 to include actual price
observations for India.7 Second, the ICP differentiates between
government expenditures and private expenditures, facilitating
international price comparisons. Finally, data collection uses the
concept of "Structured Product Descriptions," which is a list of
standardized attributes that identifies a product as narrowly as
possible, enhancing product comparability.8These detailed
descriptions allow the ICP to identify several basic headings as
comparison-resistant: government production of health
services, collective services, social protection, education, and
various medical services.

The ICP does not provide, however, a taxonomy of basic headings
as being tradable or not; indeed, developing a widely accepted
taxonomy of tradability has remained elusive.9 Thus, given the
difficulties of concisely defining tradability, we use a subjective
but, we believe, reasonable classification of basic headings as
tradable. However, one of the advantages of using the disaggregated
price data is that one can examine the implications of alternative
definitions by re-grouping the basic headings accordingly. So, our
definition is ad-hoc but it is not rigid.

2.2 Cross-Country Distributions of
Relative Prices

We measure the 2005 bilateral price level of the United States
with respect to country in basic heading as

,

(1)

where
is the 2005 market exchange
rate for country with respect to the U.S. dollar and
is the PPP exchange
rate of the basic heading in the
country, defined as
where
is the price level (local currency
per unit) of the basic heading in the country. A value of 2 for
means that the price of the
basic heading in the United States is
twice that of the same basic heading in country ,
when both are expressed in a common currency.

Given equation (1), we assemble the
cross-country distributions of relative prices for each basic
heading to examine two questions: Are the prices of a given basic
heading equalized across countries?10 Is the dispersion of
relative prices across countries related to whether the product is
tradable?

Figure 1 shows the cross-country distributions of relative
prices (
) for each basic heading; the
figure shows the basic headings that the ICP identifies as
comparison resistant and the basic headings that we identify as
tradable and non-tradable. For each distribution, we show the
median and four percentiles; these distributions are arranged in
descending order of their medians. The data show that most of the
medians are well above one, especially for comparison-resistant
products. Further, the medians of the distributions for tradable
products are generally lower than those for non-tradable products.
Finally, the dispersion of relative prices for non-tradables is
considerably larger than that for tradables. These properties
resonate with our priors that international trade tends to equate
prices across countries and that this tendency is greatest for the
most readily tradable products.

3 U.S. Relative Price Levels in
2005

We now assess the importance of the product mix for measuring
U.S. international relative price levels. To this end, we begin by
assembling the cross-country distributions of relative prices for
the largest trading partners of the United States.11
Figure 2 shows that the median for most of these distributions is
quite close to one and well below the median for the distributions
using 144 countries. To emphasize the importance of the country
mix, figure 3 compares the distributions of relative prices without
differentiating across basic headings. The figure shows that the
cross-country distribution of relative prices for U.S. trading
partners is considerably narrower and more symmetrical than the one
for the 144 countries.

To provide some perspective on what we are after, figure 4
depicts U.S. relative price levels based on the ICP's published GDP
parities for the 34 countries included in figure 2. By this
measure, U.S. GDP prices were twice as high as the GDP prices in
India and 30 percent below those in Switzerland. The question of
interest is to what extent are these measures of relative prices
influenced by the prices of basic headings that are either
non-tradable or comparison-resistant?

Addressing this question involves two steps. The first one is to
measure the aggregate relative price level between the United
States and the trading partner using alternative
basic headings. To this end, we use a weighted geometric
average:

(2)

where is a list of basic headings,
is defined in equation (1), is the share of the
country's expenditure on the basic heading, and
. A value of 2 for
means that U.S. prices are twice as
high as those in the country in list
. We consider three lists:

: All headings

: Authors' defined tradable
headings

: All headings excluding ICP's
" comparison resistant" headings

The second step is to map the into
alternative measures of the U.S. real effective exchange rate. To
this end, we use a weighted geometric mean:

(3)

where is the level of the U.S. real effective
exchange rate for list , is
defined in equation (2), and
is the U.S. bilateral trade weight
associated with the country.12 A
value of 2 for means that the aggregate of
U.S. prices in list is twice as high as the
average of aggregate prices of U.S. trading partners in the same
list.

Figure 5 reports our calculations. As a check on our procedures,
we compare the "all-headings" measure
to the published ICP's GDP
relative prices, denoted as and shown
earlier in figure 4. Excluding Thailand and Malaysia, the two
measures are very close and two factors help explain this gap.
First,
is measuring prices of domestic
expenditures whereas is measuring prices
of expenditures on domestic products-that is, excluding imports and
including exports. Second, equation (2) might differ from the one
used by the ICP.

Taking
as our benchmark of economy-wide
relative prices, we find that the relative-price measure excluding
non-tradable headings (
) shifts down the structure of
U.S. relative price levels with the shift being particularly
pronounced vis-à-vis emerging economies. For
example U.S. aggregate prices are measured to be
105 percent above those in India; whereas, if we exclude
non-tradable headings, the gap shrinks to 60 percent. In contrast,
vis-à-vis Switzerland, the measured differential shrinks by
only one percent with the exclusion of non-tradables. The
relative-price measure excluding comparison-resistant headings (
) also shifts down the structure
of relative prices, but to a lesser extent than when prices in
non-tradable headings are excluded.

The rightmost column of figure 5 shows the sensitivity of
to changes in the mix of basic
headings. Specifically, if one includes the prices of all headings
(), then U.S. prices appear to be 25
percent above the average of its trading partners. If we exclude
prices of headings that are difficult to compare across countries,
then the measured wedge shrinks to about 10 percent (). Finally, if we limit ourselves to prices for
tradable basic headings (), then there appears
to be little difference between U.S. prices and the average of
prices of its major trading partners.

This finding suggests that excluding either comparison-resistant
or non-tradable basic headings from the product mix lowers the
measure of U.S. relative prices. We do not take this finding as
evidence for designating either or
as the better measure for making
inferences about international competitiveness. Rather, we consider
the comparison-resistant and non-tradable basic headings essential
to analyzing international price positions.

Our view is not new. Indeed, Keynes noted in 1925 (p. 301): "
it is the price of sheltered [non-tradable] goods that determines
the competitiveness of a country because it is those prices that
determine the cost of producing tradable goods. The price of
unsheltered goods will be equalized by trade."13 Further, Keynes'
view is formalized by Corden (1994, p. 267) who argues that a
country's international competitiveness is determined by the
profitability in industries producing tradables. Specifically,
Corden measures international competitiveness in the industry as the ratio of the country's
price markup to that of the United States:

(4)

where is the dollar price of the
tradable industry in the
country, and is the associated marginal cost,
also in dollars. Thus, if
, then the
country is said to be more competitive than the United States
because it has a higher price markup. Further, if one assumes that
international trade equalizes prices of tradable products, then

(5)

Again, if
, then the
country is more competitive than the United States because it has
lower marginal costs. Marginal costs are directly related to factor
prices, such as wages that are, in turn, directly related to the
importance of non-tradables (e.g. housing, medical services) in
domestic expenditures. Given that comparison-resistant and
non-tradable basic headings account for more than half of U.S.
total domestic expenditures (figure 6), abstracting from them
yields an incomplete characterization of international
competitiveness.

4 Development and Relative Price
Levels

In this section we study the correlation between the level of
economic development and the level of relative prices across
countries, known as the Penn Effect. Intuitively, higher levels of
income raise the demands for tradable and non-tradable goods and
services. The higher demand for tradables is met through
international trade with no change in tradable's prices. But the
higher demand for non-tradables is met by the fixed, local supply,
raising the price of non-tradables and, thus, the overall price
level. So the natural question to ask is whether the data support
the view that an increase in income raises the relative prices of
non-tradable categories.

To this end, we begin by replicating the Penn Effect and
postulate that

(6)

where

is the U.S. price relative
to the price of the country using ICP's
published GDP parities

is the GDP of the country

is the population of the
country

For the conventional explanation of the Penn Effect to be
consistent with the aggregate data, one needs to find that
: An increase in the per-capita
income of the country relative to U.S. per-capita
income raises the price in the country relative
to the corresponding U.S. price and, hence, lowers . The regression yields

where the standard errors of the coefficients are corrected for
potential heteroskedasticity of the residuals.14 The result
confirms that when using the ICP's published
parities for GDP.

To examine whether this correlation holds at the level of basic
headings, we use

(7)

where
and
is defined in equation
(1). For the conventional explanation of the
Penn Effect to be consistent with the data at the disaggregate
level, one needs to find that
An increase in the
per-capita income of the country relative to U.S.
per-capita income tends to raise the price of the good in the country relative to the
corresponding U.S. price, which then lowers
. Thus finding that
for non-tradables would
undermine the usefulness of the conventional explanation for the
Penn Effect.

Figure 7 shows the estimates of and
their 95 percent confidence bands.15 For the vast majority
of basic headings, the estimated is
negative and significantly different from zero. That is, for most
of the basic headings, higher prices in the
country are associated with higher incomes in the country. We also note that the estimates of tend to be larger (in absolute value) for the
headings that we denoted non-tradables than for the headings we
denoted tradables. This finding strengthens the empirical support
of the conventional explanation of the Penn Effect.

This pattern for the s is not a necessary
consequence of the pattern seen in figure 1, as the estimated
intercept could absorb the variation in the medians. Indeed, the
estimated standard errors of the regressions bear no relationship
to the ordering of the basic headings (figure 8). Finally, note
that for three of these products (motorcars, motorcycles, and
passenger transport by air), the estimated is
significantly positive, meaning that higher prices are associated
with lower incomes, a deviation from the Penn Effect. This
seemingly contradictory finding might be the result of some
countries treating these products as luxuries and thus levying
taxes on them.

5 Conclusions

The view under the hood yields two insights that might be useful
for practical analyses and further research.

First, we get a good sense of the extent to which the real
effective exchange rate for the United States is affected by the
inclusion of non-tradable prices. For 2005, with the full product
list, the U.S. REER shows U.S. prices to be more than 20 percent
above those of its trading partners, while for tradable products
alone, there is little difference between U.S. prices and those of
its trading partners. We do not view this sensitivity as an
argument for excluding non-tradables when judging competitiveness
because the prices of non-tradables are central to determining a
country's profitability in tradable products.

Second, the Penn Effect is not an artifact of aggregation.
Indeed we find that this effect holds for the majority of basic
headings. Interest in this disaggregation is not new but previous
work uses aggregate price indexes for selected sectors of
industrial countries. In contrast, we offer evidence based on
relative price levels (as opposed to indexes) of 126 basic
headings for 144 countries that differ greatly in their level of
development. This generality makes the Penn Effect an interesting
subject for future research because it does not rely on aggregation
formulas.

Footnotes

* The views in this paper are solely the
responsibility of the authors and should not be interpreted as
reflecting the views of the Board of Governors of the Federal
Reserve System or of any other person associated with the Federal
Reserve System. We are grateful to Nada Hamadeh for providing the
ICP data and to both Fred Vogel and D.S. Prasada Rao for numerous
comments. We are also grateful to Rudolfs Bems, Neil Ericsson, and
to participants in previous presentations of this paper at George
Washington University, the meetings of the Fall 2009 Midwest
International Economics Group (Penn State), the Fall 2009 and
Spring 2012 Workshops of the Federal Reserve Board, the 58th World
Statistical Congress of the International Statistical Institute
(Ireland, August 2011), and the 2012 IMF's Research Seminar series.
The regression results use OxMetrics 6.20; see Doornik and Hendry
(2007). Return to text

1. The views in this paper are solely the
responsibility of the authors and should not be interpreted as
reflecting the views of the Board of Governors of the Federal
Reserve System or of any other person associated with the Federal
Reserve System. We are grateful to Nada Hamadeh for providing the
ICP data and to both Fred Vogel and D.S. Prasada Rao for numerous
comments. We are also grateful to Rudolfs Bems, Neil Ericsson, and
to participants in previous presentations of this paper at George
Washington University, the meetings of the Fall 2009 Midwest
International Economics Group (Penn State), the Fall 2009 and
Spring 2012 Workshops of the Federal Reserve Board, the 58th World
Statistical Congress of the International Statistical Institute
(Ireland, August 2011), and the 2012 IMF's Research Seminar series.
The material presented here draws from, and extends, the analysis
in Thomas et al. (2011). The regression results use OxMetrics 6.20;
see Doornik and Hendry (2007). Return to
text

2. For reviews on the measurement of real
effective exchange rates, see Froot and Rogoff (1995), Taylor
(2003), Chinn (2005), Klau and Fung (2006); other relevant papers
include Lipsey, Molinari, and Kravis (1990), Hooper and Richardson
(1991), and Turner and Van't dac (1993). For the relation between
prices and development, see Kravis, Heston, and Summers (1978);
Summers and Heston (1991); Asea and Mendoza (1994); De Gregorio,
Giovannini and Wolf (1994); Canzoneri, Cumbi and Diba (1996);
Bergin, Glick, and Taylor (2006); Heston, Summers, and Aten (2006);
Lothian and Taylor (2008); and Ravalion (2010). Return to text

9. De Gregorio et al. (1994) define a
product as tradable if at least 10 percent of the value of its
production "worldwide" is exported. DeGregorio et al. examine 20
production sectors for a world consisting of 14 industrial
countries. The practical appeal of their definition diminishes as
soon as one expands the list of countries included in the world and
uses disaggregated expenditure categories, which is what we do
here. Return to text

12. We use the weighting scheme adopted by
the Federal Reserve (Leahy, 1998). In this scheme, the
un-normalized broad weight for a given country is
where is the share of non-oil imports from
the country; is the
export share to the country; and
is the extent to which exports
to the country compete with exports from other
countries; the normalized broad weight of the
country is
The data
come from the U.S. Commerce Department. Return to text

13. Of course, productivity differentials
also figure importantly into the mapping from the prices of
non-tradables to the cost of producing tradables. Unfortunately,
broad, cross-country data that compare the levels of productivity
are not available. Return to
text

14. The regression statistics are SER:
0.289;
0.55. The Jarque-Bera test
for normality is 4.3466 and one cannot reject the hypothesis that
the residuals are normally distributed at the 5 percent
significance level. Return to
text